PRACTICAL 4: Transient Conduction
Concept questions
C1. Consider a hot baked potato on a plate. The temperature of the potato is observed to drop by 4oC during the first minute. Will the temperature drop during the second minute be less than, equal to, or more than 4oC? Why?
C2. Consider heat transfer between two identical hot solid bodies and their environments. The first solid is dropped in a large container filled with water, while the second one is allowed to cool naturally in the air. For which solid is the lumped system analysis more likely to be applicable? Why?
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1. Long carbon steel (AISI 1010) shafts of 0.1 m diameter are heat treated in a gas-fired furnace whose gases are 1200 K, with a convection coefficient of 100 Wm-2 K-1. If the shafts enter the furnace at 300 K:
a. how long must they remain in the furnace to achieve the required centerline temperature of 800K?
b. what will be the surface temperature of the shafts after that time?
2. Stainless steel (AISI 304) ball bearings, which have been uniformly heated to 850 oC, are hardened by quenching them in an oil bath that is maintained at 40 oC. The ball diameter is 20 mm and the convection coefficient associated with the oil bath is 1000 Wm-2 K-1. If quenching is to occur until the surface temperature of the balls reaches 100 oC, calculate:
a. What is the centre temperature of the balls when the surface temperature reaches 100 oC?
b. How long must the balls be immersed for the surface temperature to reach 100oC?
c. How much energy is lost from each ball during quenching?
d. If 10 000 balls per hour are quenched, what is the rate at which energy must be removed by the oil bath cooling system in order to maintain the bath temperature at 40 oC?
3. In a manufacturing process, long rods of different diameters are heated to a uniform temperature of 400 oC in an oven, from which they are removed and cooled by forced convection in air at 25 oC. One of the line operators has observed that it takes about 200 seconds for a 8-mm diameter rod to cool to a safe-to-touch temperature of 60 oC. The thermo-physical properties of the rods are =2500 kg m-3, Cp=900 Jkg-1K-1, k=10 Wm-1K-1.
a. Calculate the heat transfer coefficient for convection from the rod to the air (note: test any assumptions which you have made, and comment on whether the value seams realistic)
Now consider an 80 mm diameter rod made from the same material:
b. What will be the centerline temperature of the 80 mm diameter rod when the surface reaches the safe-to-touch temperature of 60 oC?
c. How long will it take for the rod to cool to the safe-to-touch surface temperature?
d. How much heat will be lost from the 8 mm diameter rod during the first minute of cooling, and what will be the surface temperature of the rod after that time?
e. How much heat will be lost from the 80 mm diameter rod during the first minute of cooling, and what will be the surface temperature of the rod after that time? Compare with the thinner rod.
f. How valid is your assumption to neglect radiation? (compare the heat flux due to convection and radiation of the rods at 400 oC, assuming that the emissivity of the rods is 0.25)
BONUS MARK QUESTION Based on the thermo-physical properties, can you estimate what type of material the rods are made from?
4. You have just arrived at the scene of a crime, to which there are only 2 witnesses. The crime occurred in the kitchen, and dinner plates containing food are on the kitchen table. The two witnesses agree that the crime was committed just as dinner was put on the table, but they disagree about how long ago that occurred. Witness A said that the dinner was served (and the crime committed) 15 minutes prior to your arrival; Witness B claims that these events took place more than an hour ago. Having studied heat transfer, you realize that the potatoes provide the clue to the mystery, and quickly measure the diameter (8 cm) and surface temperature (40oC) of the boiled potatoes on the dinner plates. The air temperature in the kitchen is 20oC, and you have calculated the coefficient for heat transfer from the potatoes to be 5 Wm-2K-1.
a. Assuming that the potatoes were at a uniform temperature of 100oC when they were placed on the plate, how long since dinner was served?
b. You will need to present this evidence in court, so you also measure the temperature of the centre of the potato to validate your model; what do you predict that temperature to be?
c. Since your calculations could be used to send someone to jail, you must indicate an uncertainty, i.e. put a range on your estimate of how long prior to your arrival the dinner was served, accounting for the fact that the potatoes could have been only 80oC when served, and that h has an uncertainty of +/- 50%. Also comment on any other assumptions which might affect your predictions.
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